Asymptotic analysis in thermodynamics of viscous fluids

We discuss some recent results in the mathematical theory of complex fluid systems, in particular, the concept of weak solution and its relevance to a proper formulation of balance laws in fluid mechanics.
A rigorous asymptotic analysis of these systems is developed and several model problems discussed.
In particular, the following topics will be addressed in detail:

functional analytic framework and the basic ideas of the mathematical theory of continuum fluid mechanics;

thermodynamic stability and equilibrium states, behavior of energetically insulated systems for large time;

low Mach number limits and propagation of acoustic waves in thermally conducting viscous fluids.